Strain localization driven by structural relaxation in sheared amorphous solids.

A two dimensional amorphous material is modeled as an assembly of mesoscopic elemental pieces coupled together to form an elastically coherent structure. Plasticity is introduced as the existence of different minima in the energy landscape of the elemental constituents. Upon the application of an external strain rate, the material shears through the appearance of elemental slip events with quadrupolar symmetry. When the energy landscape of the elemental constituents is kept fixed, the slip events distribute uniformly throughout the sample, producing on average a uniform deformation. However, when the energy landscape at different spatial positions can be rearranged dynamically to account for structural relaxation, the system develops inhomogeneous deformation in the form of shear bands at low shear rates, and stick-slip-like motion at the shear bands for the lowest shear rates. The origin of strain localization is traced back to a region of negative correlation between strain rate and stress, which appears only if structural relaxation is present. The model also reproduces other well known effects in the rheology of amorphous materials, as a stress peak in a strain rate controlled experiment staring from rest, and the increase of the maximum of this peak with sample age.